Fund managers who actively pick stocks rather than passively
follow an index of companies have long taken a beating. A
long line of studies has shown that the majority of active
mutual funds—weighed down by high charges and expenses—
yield low returns relative to comparable passive funds. For instance,
a study finds that in the past 23 years an aggregate portfolio of
active equity mutual funds in the United States underperformed
various benchmarks by about one percent a year. Most active fund
managers who succeed in beating the market in one year tend to
fail in the next, dashing investors' hopes that there is more to a
manager's stellar performance than just good luck. Altogether, the
evidence firmly suggests that for most investors it does not pay to
seek the skills of an active manager.

Yet the active funds industry remains large, with investors
choosing to put far more of their financial assets in active rather
than passive funds. Despite the robust growth in index-style mutual
funds, the Investment Company Institute notes that, at the end of
2008, about 87 percent of all assets in equity mutual funds were
actively managed. Even institutional investors, who seem more
inclined than retail investors to invest passively, put at least half of
their US equity investments in active funds.

A number of explanations have been offered for this puzzling
result, many of which suggest that investors are not very smart.
Investors may be fooled by slick fund management firms that
manipulate past performance numbers to make their funds look
like winners, or investors may stubbornly believe that they know
which active managers have real, sustained skills in stock picking.

But a recent study titled, "On the Size of the Active Management
Industry," by Chicago Booth professor Lubos Pastor and Robert F.
Stambaugh of the University of Pennsylvania, finds that the large
size of the active management industry could result from sensible
actions of smart investors. In particular, investors understand that a manager's ability to outperform passive funds increases as
the active management industry becomes smaller and decreases
as the industry grows. This inverse relationship between size and
performance has prevented the industry from disappearing decades
ago, as its poor record would have predicted.

Why the Active Management Industry Is Large
What is unique about Pastor and Stambaugh's paper is that it
assumes that the active management industry exhibits decreasing
returns to scale; that is, as the industry grows, more money chases
opportunities to outperform the market, which makes it harder
for active managers to find bargain-priced stocks for their clients.
If the industry shrinks, on the other hand, then less competition
among the remaining managers gives them a better chance of
finding mispriced stocks and offering clients higher returns.

This view implies that the industry's alpha, which is the
expected return from investing in active funds in excess of the
return on benchmark index funds, is not constant. Instead, alpha
decreases as the active management industry grows and increases
as the industry shrinks. The inverse
relationship between industry size and alpha, say Pastor and
Stambaugh, is the key to understanding the immense popularity
of active management.

Investors think about alpha when deciding how much money
to invest in active funds. They do not know what alpha exactly
is, but they can learn about it by observing the returns of active
fund managers. If these returns turn out to be disappointing, for
instance, then investors update their views about alpha downward
and reduce their investment in active funds.

However, they will not pull out all of their money. The belief
that future returns are inversely related to the size of the industry
cushions the fall in the share of financial assets that goes into active funds. Rational investors know that if other people withdraw their
money, too, then it will be easier for active managers who represent
the remaining investors to find good deals and generate higher
returns. Because a reduction in the size of this industry implies a
higher alpha, investors will take out some of their money but keep
a substantial amount invested in active funds to take advantage of
higher expected returns. If all investors think the same way, then it
is easy to see how the industry may gradually become smaller over
time but still remain a formidable presence.

In fact, the authors find that the share of active funds in total
financial assets can exceed 70 percent even if the industry's alpha
is significantly negative. Given the observed history of active
mutual fund returns, the smart investor's allocation to active funds
drops very slowly over time, from about 90 percent in 1962 to 70
percent in 2006. This striking result shows that, although the active
management industry should be smaller—due to its weak past
performance—it can still remain large.

Investors would have withdrawn more money from active funds
had they believed that the size of the industry had no impact on
alpha. Under this more traditional assumption of constant returns
to scale, the authors find that the active industry's poor record
would have led to its quick demise, disappearing altogether in 1969.

Rational but Slow
Although investors know that future returns tend to rise and
fall with the size of the active management industry, they do not
know the exact correlation between these two variables. This is
because the industry's size varies little from one period to the
next. "The size of the industry doesn't fluctuate wildly, and when
a variable changes slowly, it's very hard for investors to figure out
its impact on alpha," says Pastor.

Investors learn slowly about the precise relationship between
industry size and returns, and that uncertainty affects their
decision regarding how much of their financial assets will go into
active funds. For instance, if investors see that the actual return
on active funds is lower than expected, they will reduce their
active fund allocation; however, because investors do not know
exactly how their actions and those of other investors will affect
alpha, they will be reluctant to make large changes. Investors will
proceed more cautiously by not taking as much money out of
active funds as they would if they fully understood the correlation
between industry size and return. As a result, the active
management industry becomes smaller but not by very much.

Small changes in the size of the active management industry,
in turn, make learning about decreasing returns to scale more
difficult than if investors made large changes to their active funds
allocations. The result is a vicious cycle—investors tweak their
allocations to active funds slowly because they are uncertain about
how steep returns to scale are, but they learn about the returns to
scale slowly because the industry hardly changes in size.

The result is an active funds industry that is smaller over time,
but remains enormous even after many years of underperformance.
"Of course, investors are not perfectly rational," Pastor says. "But
even if they were, they would still find it optimal to keep a chunk of
their money in active funds."

"On the Size of the Active Management Industry." Lubos Pastor and Robert F. Stambaugh. Working paper, 2012.